In August 1646 John Winthrop, governor of the Massachusetts Bay Colony, noted that the ministers of the United Colonies (MBC, Plymouth, Connecticut, New Haven) were meeting at a synod. But the powerful church of Boston, Winthrop noted, did not send its mighty and respected minister (John Cotton) or teacher (John Wilson).
"Boston [took] offence," wrote Winthrop. "[They] inferred that this synod was appointed by the [church] elders to make ecclesiastical laws to bind the Churches and to have the sanction of the civil authority put upon them, whereby men should be forced under penalty to submit to them. Whereupon they concluded that they should betray the liberty of the Churches if they should consent to such a synod."
This is the polar opposite of what most Americans believe the Puritans' stance toward church and state to be.
Winthrop is saying that it is completely unacceptable to have civil laws about religion, because then two bad things happen: the state controls the church, and citizens can be punished in civil courts for their religious choices.
We like to think that Puritan officials were constantly poking into peoples' private lives. There was poking, to be sure, but it was done strictly by ministers and elders, not by lawmakers. (And most of that poking was at the urging of a public that was extremely dedicated to maintaining the Puritan system.)
The General Court was the Puritans' civil legislature. It had no authority over the churches. In turn, the clergy could not become members of the Court. Church and state were completely separate, and while there was some wavering on this point, the Court's authority was stronger than the churches' authority.
One of the things the MBC Puritans feared most was that the English government would take control of the colony and begin administering the churches, making laws about church policies and making clergy appointments.
Certainly the Puritans believed church polity was crucial to any working society. But church polity was held totally separate from civic politics; they were two different worlds. This attitude remained firmly entrenched in New England for centuries to come.